Question: Multiply the following complex numbers: $({-3+3i}) \cdot ({-2+3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+3i}) \cdot ({-2+3i}) = $ $ ({-3} \cdot {-2}) + ({-3} \cdot {3}i) + ({3}i \cdot {-2}) + ({3}i \cdot {3}i) $ Then simplify the terms: $ (6) + (-9i) + (-6i) + (9 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 6 + (-9 - 6)i + 9i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 6 + (-9 - 6)i - 9 $ The result is simplified: $ (6 - 9) + (-15i) = -3-15i $